OPTIMAL ORDER MULTIGRID METHODS FOR SOLVING EXTERIOR BOUNDARY-VALUE-PROBLEMS

The coupling of boundary elements and finite elements combines the adv antage of boundary elements for treating domains extended to infinity and that of finite elements in treating the nonhomogeneity of equation s and the complexity of domains. In the case of the Laplacian, by taki ng a circle or a sphere as the artificial coupling boundary, it is sho wn that the corresponding boundary integral equation can be solved wit hout any cost and the coupled system is reduced to a simple finite ele ment system. Two multigrid methods are proposed to solve this finite e lement linear system. Both methods are of optimal order and can be use d to solve such finite element equations as efficiently as to solve th ose arising from interior boundary value problems. Numerical experimen ts are included to show the efficiency and advantages of the methods. An apparent significance of the methods is that the boundary elements appear neither in the discretization nor in the coding.